(As pointed out in [1]}, the strict pullback is a homotopy pullback here because \(X\)  is Reedy fibrant.)
Consider the commutative diagram
\(\begin{tikzcd}[column sep=2cm, row sep=1.5cm]X_n [r]& X_1 \underset{X_0}{\times } \cdots \underset{X_0}{\times } X_1\\X_0 [u, "s"] [r, "{(1_{X_0}, \ldots , 1_{X_0})}"^{\prime }, "\cong "]& X_0 \underset{X_0}{\times } \cdots \underset{X_0}{\times } X_0 [u, "s_0 \times \cdots \times s_0"^{\prime }]\end{tikzcd}\) 
